Session F3a: Lunar Positioning, Navigation, and Timing

Orbit Determination of Lunar Radio Navigation Satellites Using MEMS Accelerometers and Microwave Tracking
Luciano Iess and Andrea Sesta, Sapienza University of Rome
Alternate Number 1

The performances of a lunar radio navigation system depend on a precise orbit determination and time synchronization (ODTS) system. In a prior study [1], we introduced a system architecture centered on the concept of Multiple Spacecraft per Aperture (MSPA). In this framework, a constellation of small satellites (smallsats) is tracked in two-way coherent mode from a single ground antenna, yielding highly accurate range, range rate, and single-beam interferometry (SBI) measurements crucial for orbit determination. The preferred frequency of the link is in K band (22.5-26.5 GHz) to reduce ionospheric effects and use larger modulation bandwidths enabling more accurate ranging measurements.
While the proposed system is able to meet all positioning and time synchronization requirements set by the agencies (in particular the European Space Agency - ESA) the orbit determination analysis found that the ageing of the navigation message, in particular the ageing of the ephemerides, is relatively fast. This is a consequence of the relatively large area-to-mass ratio of the satellites of the constellation, based on smallsats. The satellites are therefore subject to quite large non-gravitational accelerations (NGA), with solar radiation pressure dominating over thermal recoil and other weaker effects.
In this work, we assess the benefits and limitations of a direct measurement of NGA by means of low mass, low power, MEMS-bases accelerometers under development in Europe. Although the TRL level of these units is still low, we use the predicted performances, at two levels of their development stages, to improve the orbit determination and the propagation of the spacecraft state. In the first stage, the target for the acceleration noise floor is 3x10^(-8) m/s^2/Hz^(1/2) at 10^(-4) Hz, and 3x10^(-7) m/s^2/Hz^(1/2) at 10^(-5) Hz. In a further development, the target acceleration noise floor is one order of magnitude lower (see table 1). At 10^(-4) Hz the noise floor is about 1% and 0.1% of the total expected solar radiation pressure acceleration, respectively for stages 1 and 2 of the MEMS accelerometer development. Given that the orbital period of the satellites is about 24 h, the performances at low frequency are especially relevant.
Numerical simulations indicate that even a low-rate transmission to ground of the three components of the measured acceleration (one vectorial acceleration every 60 s) may improve the accuracy of orbit determination if the advanced version of the accelerometer is used. However, only a further improvement by a factor of 10 in the noise floor of the accelerometer at low frequencies (10^(-5) – 10^(-3) Hz) would result in a major advantage over mathematical modelling of non-gravitational accelerations.
While accelerometers may contribute to a better orbit reconstruction, therefore extending the validity period of the navigation message, the main factor causing the ageing of the ephemerides, i.e. the inaccurate modelling of the NGA, still persists. We propose to tackle this problem with two methods, both requiring an analysis and training period. In the first method, the accelerometer data are used to refine the model of the NGA adopted in the determination and propagation of the orbit. An optimization process based upon the comparison between the measured and estimated NGA, relying on an accurate model of the spacecraft shape and shadowing effects, would allow to estimate the free parameters of the model more accurately than it is possible with radio-metric data. Additionally, accelerometer measurements can refine and validate the spacecraft's thermal model, crucial for inferring thermal recoil. In a different approach, the NGA model integrates physics-informed machine learning methods trained on the measured accelerations. While the actual training will be carried out once the constellation will be deployed, it is still possible to test the benefits of this approach by using a simulated accelerometer data set.
[1] Iess, L., Di Benedetto, M., Boscagli, G., Racioppa, P., Sesta, A., De Marchi, F., ... & Ventura-Traveset, J. (2023, September). High Performance Orbit Determination and Time Synchronization for Lunar Radio Navigation Systems. In Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023) (pp. 4029-4050).